A positron CT apparatus, i.e. a PET (Positron Emission Tomography) apparatus, is constructed to detect two gamma rays generated by annihilation of positive electrons (positrons), and reconstruct an image of the subject only when a plurality of detectors detect gamma rays at the same time (that is, only when coincidences are counted).
With this PET apparatus, quantitative measurement of various living body functions is possible by serially measuring a process of drug accumulation in target tissue after introducing a radioactive drug into the subject. Therefore, images obtained by the PET apparatus have functional information.
Specifically, to describe this by taking a small animal (e.g. a mouse) as an example of subject, a positron (positive electron) emitting isotope (e.g. 15O, 18F, 11C, or the like) is injected into the body of the subject, and gamma rays generating when the positrons released from these combine with electrons are detected. The detection of these gamma rays is carried out with a detector array consisting of numerous gamma-ray detectors. And a computer carries out image reconstruction to create images of the subject.
The following technique is used when reconstructing images (see Nonpatent Documents 1 and 2, for example). First, pixels formed of 3D voxels in a field of view (FOV) are expressed by νj (j=0, 1, . . . , J−1), and an i-th LOR (Line Of Response) by Li (i=0, 1, . . . , I−1). LOR refers to a virtual straight line linking two detectors that carry out coincidence counting. Where pixels consist of 3D voxels, LOR refers to a tubular region linking two detectors having detected two gamma-ray photons generating from each voxel and emitted in opposite directions.
Now, in reconstruction of a PET image, probability aij that gamma-ray photons generating from voxels νj will be detected on LOR (Li) plays an important role. This aij is called “system matrix”. See Nonpatent Documents 1 and 2 for formulization of image reconstruction.
The number (count value) of photons is measured using a point source which emits the same type of radiation as a positron-emitting drug. A profile of the number of photons with respect to distances from the point source is obtained, and is adjusted by fitting it to a Gauss function or the like, thereby to obtain a point spread function (PSF). Then, can be obtained by assuming that detection probability is proportional to the point spread function (hereinafter abbreviated to “PSF” as appropriate) (see Nonpatent Document 3, for example).
However, when the PSF obtained from the fitting is used as it is, an overcorrection phenomenon (e.g. ringing adjacent boundaries of the subject) appears due to errors in geometric calculations in the reconstruction calculations, or statistical errors included in the data for reconstruction. It is known that, in order to inhibit this overcorrection phenomenon, aij needs to be calculated by narrowing by a fixed quantity the spread of the PSF obtained from actual measurement (see Nonpatent Document 4, for example).
Specifically, the distance range of the PSF may be adjusted by adjusting to change the full width at half maximum (FWHM) or distribution of the Gauss function. When the Gauss function is expressed by αexp {−(x−b)2/2c2}, the full width at half maximum (FWHM) is a value of an entire width corresponding to a half value of local maximal value (peak) of the Gauss function, which is expressed by 2 √(2 ln 2)·c.
Incidentally, in recent years, in order to improve the spatial resolution of images, detectors consisting of scintillator elements arranged in three dimensions have been used in PET apparatus (see Nonpatent Document 5, for example). Specifically, a PET apparatus has, incorporated therein, DOI detectors which can discriminate positions in depth directions (DOI: Depth of Interaction) where interaction has occurred. The DOI detectors are constructed by stacking scintillator elements in the depth directions of radiation (gamma rays here), and coordinate information on the depth directions and transverse directions (directions parallel to the planes of incidence) which caused the interaction is obtained by centroid calculation. By using the DOI detectors, it becomes possible to inhibit resolution degradation at peripheries of the field of view.